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Progress In Electromagnetics Research
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THE METHODS OF EXTERNAL EXCITATION FOR ANALYSIS OF ARBITRARILY-SHAPED HOLLOW CONDUCTING WAVEGUIDES

By S. Y. Reutskiy

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Abstract:
A new numerical technique is proposed for analyzing arbitrary shaped hollow waveguides. The method is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. The results of the numerical experiments justifying the method are presented. The method is validated by circular waveguide,rectangular waveguide an equilateral triangular waveguide. We apply the method for multi connected domains and for waveguides with boundary singularities like the Lshaped waveguide. Good agreements between the simulated and the published results have been obtained. The method does not generate spurious eigenfrequencies.

Citation:
S. Y. Reutskiy, " the methods of external excitation for analysis of arbitrarily - shaped hollow conducting waveguides ," Progress In Electromagnetics Research, Vol. 82, 203-226, 2008.
doi:10.2528/PIER08022701
http://www.jpier.org/PIER/pier.php?paper=08022701

References:
1. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, 1953.

2. Bulley, R. M., "Analysis of arbitrary shaped waveguide by polynomial approximation," IEEE Trans. Microwave Theory Tech., Vol. 18, No. 12, 1022-1028, 1970.
doi:10.1109/TMTT.1970.1127406

3. Lin, W. K., L. W. Li, T. S. Yeo, and M. S. Leong, "Analysis of metallic waveguides of large class of cross sections using polynomial approximation and superquadric functions," IEEE Trans. Microwave Theory Tech., Vol. 49, No. 6, 1136-1239, 2001.
doi:10.1109/22.925504

4. Tomas, D. T., "Functional approximations for solving boundary value problems by computer," IEEE Trans. Microwave Theory Tech., Vol. 17, No. 8, 447-454, 1969.
doi:10.1109/TMTT.1969.1126995

5. Swaminathan, M., Arvas, T. K. Sarkar, and A. R. Djordjevic, "Computation of cutoff wavenumbers of TE and TM modes in waveguides of arbitrary cross sections using a surface integral formulation," IEEE Trans. Microwave Theory Tech., Vol. 38, No. 2, 154-159, 1990.
doi:10.1109/22.46425

6. Guan, J. M. and C. C. Su, "Analysis of metallic waveguides with rectangular boundaries by using the finite-difference method and the simultaneous iteration with the Chebyshev acceleration," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 2, 374-382, 1995.
doi:10.1109/22.348098

7. Hernandez-Lopez, M. A. and M. Quintillan-Gonzalez, "A finite element method code to analyze waveguide dispersion," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 397-408, 2007.
doi:10.1163/156939307779367396

8. Yener, N., "Algebraic function approximation in eigenvalue problems of lossless metallic waveguides: Examples," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 731-745, 2006.
doi:10.1163/156939306776143442

9. Yener, N., "Advancement of algebraic function approximation in eigenvalue problems of lossless metallic waveguides to infinite dimensions," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1611-1628, 2006.
doi:10.1163/156939306779292363

10. Khalaj-Amirhosseini, M., "Analysis of longitudinally inhomogeneous waveguides using Taylor’s series expansion," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 8, 1093-1100, 2006.
doi:10.1163/156939306776930286

11. Khalaj-Amirhosseini, M., "Analysis of longitudinally inhomogeneous waveguides using the Fourier series expansion," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1299-1310, 2006.
doi:10.1163/156939306779276758

12. Xiao, J.-K., W.-S. Ji, S. Zhang, and Y. Li, "A field theoretical method for analyzing microwave cavity with arbitrary crosssection," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 4, 435-446, 2006.
doi:10.1163/156939306776117054

13. Mei, Z. L. and F. Y. Xu, "A simple, fast and accurate method for calculating cutoff wavelengths for the dominant mode in elliptical waveguide," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 367-374, 2007.
doi:10.1163/156939307779367440

14. Yung, E. K. N. and W. Lin, "Theory of Cassinian waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 10, 1323-1331, 2007.
doi:10.1163/156939307783239483

15. Shu, C. and Y. T. Chew, "Application of multi-domain GDQ method to analysis of waveguides with rectangular boundaries," Progress In Electromagnetic Research, Vol. 21, 1-19, 1999.
doi:10.2528/PIER98052601

16. Shu, C., W. X. Wu, and C. M. Wang, "Analysis of metallic waveguides using least square-based finite difference method," CMC: Computers, Materials & Continua, Vol. 2, 189-200, 2005.

17. Ooi, B. L. and G. Zhao, "Element-free method for analysis of arbitrarily-shaped hollow conducting waveguides," IEE Proceedings --- Microwaves, Antennas and Propagation, Vol. 152, No. 1, 31-34, 2005.
doi:10.1049/ip-map:20045009

18. Zhao, G., B. L. Ooi, Y. J. Fan, Y. Q. Zhang, I. Ang, and Y. Gao, "Application of conformal meshless RBF coupled with coordinate transformation for arbitrary waveguide analysis," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 1, 3-14, 2007.
doi:10.1121/1.403714

19. Kondapalli, P. S. and D. J. Shippy, "Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions," Journal of the Acoustical Society of America, Vol. 91, No. 4, 1844-1854, 1992.
doi:10.1016/S0893-9659(01)00053-2

20. Karageorghis, A., "The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation," Applied Math. Letters, Vol. 14, 837-842, 2001.

21. Chen, J. T., J. H. Lin, S. R. Kuo, and S. W. Chyuan, "Boundary element analysis for the Helmholtz eigenvalues problems with a multiply connected domain," Proc. R. Soc. Lond. A, Vol. 457, 2521-2546, 2001.

22. Chen, J. T., L. W. Liu, and H. K. Hong, "Spurious and true eigensolutions of Helmholtz BIEs and BEMs for a multiply connected problem," Proc. R. Soc. Lond. A, Vol. 459, 1897-1924, 2003.
doi:10.1006/jsvi.2002.5038

23. Chen, J. T., M. H. Chang, K. H. Chen, S. R. Lin, and , "The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function," Journal of Sound and Vibration, Vol. 257, 667-711, 2002.
doi:10.1016/j.enganabound.2004.10.005

24. Chen, J. T., L. Chen, and Y. T. Lee, "Eigensolutions of multiply connected membranes using the method of fundamental solutions," Engineering Analysis with Boundary Elements, Vol. 29, 166-174, 2005.
doi:10.1163/156939306779292174

25. Bucci, O. M., G. D’Elia, and M. Santojanni, "A fast multipole approach to 2D scattering evaluation based on a non redundant implementation of the method of auxiliary sources," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1715-1723, 2006.
doi:10.2528/PIER04072101

26. Anastassiu, H. T., "Error estimation of the method of auxiliary sources (MAS) for scattering from an impedance circular cylinder," Progress In Electromagnetics Research, Vol. 52, 109-128, 2005.
doi:10.1163/156939307783152920

27. Liu, X., Z. Wang, and S. Lai, "Element-free Galerkin method in electromagnetic scattering field computation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1915-1923, 2007.
doi:10.1163/156939307779378772

28. Ooi, B. L. and G. Zhao, "Element-free method for the analysis of partially-filled dielectric waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 189-198, 2007.
doi:10.1016/j.enganabound.2005.10.006

29. Li, Z. C., T. T. Lu, H. Y. Hu, H. S. Tsai, and A. H. D. Cheng, "The Trefftz method for solving eigenvalue problems," Engineering Analysis with Boundary Elements, Vol. 30, 292-308, 2006.
doi:10.1016/j.enganabound.2005.08.011

30. Reutskiy, S. Y., "The method of fundamental solutions for Helmholtz eigenvalue problems in simply and multiply connected domains," Engineering Analysis with Boundary Elements, Vol. 30, 150-159, 2006.

31. Reutskiy, S. Y., "The method of fundamental solutions for eigenproblems with Laplace and biharmonic operators," CMC: Computers, Materials Continua, Vol. 2, 177-188, 2005.

32. Reutskiy, S. Y., "The Method of External Sources (MES) for eigenvalue problems with Helmholtz equation," CMES: Computer Modeling in Engineering & Sciences, Vol. 12, 27-39, 2006.
doi:10.1016/j.enganabound.2007.04.003

33. Reutskiy, S. Y., "The methods of external and internal excitation for problems of free vibrations of non-homogeneous membranes," Engineering Analysis with Boundary Elements, Vol. 31, 906-918, 2007.

34. Reutskiy, S. Y., "The Method of External Excitation for problems of free vibrations of non-homogeneous Timoshenko beams," International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 8, 10-21, 2007.
doi:10.1016/S0955-7997(02)00017-6

35. Chen, W., "Symmetric boundary knot method," Engineering Analysis with Boundary Elements, Vol. 26, 489-494, 2002.
doi:10.1016/j.cma.2007.02.004

36. Chen, J. T., C. T. Chen, P . Y. Chen, and I. L. Chen, "A semi-analytical approach for radiation and scattering problems with circular boundaries," Computer Methods in Applied Mechanics and Engineering, Vol. 196, 2751-2764, 2007.

37. Alves, C. J. S. and P. R. S. Antunes, "The method of fundamental solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes," CMC: Computers, Materials & Continua, Vol. 2, 251-266, 2005.
doi:10.1137/0704008

38. Fox, L., P. Henrici, and C. Molor, "Approximations and bounds for eigenvalues of elliptic operators," SIAM J. Numer. Anal., Vol. 4, 89-102, 1967.
doi:10.1137/S0036144503437336

39. Betcke, T. and L. N. Trefethen, "Reviving the method of particular solutions," SIAM Review, Vol. 47, 469-491, 2005.

40. Trefethen, L. N. and T. Betcke, "Computed eigenmodes of planar regions," AMS Contemporary Mathematics, Vol. 412, 297-314, 2006.

41. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipescipes in C++, 2nd Ed., Cambridge University Press, 2002.
doi:10.1070/RM1967v022n02ABEH001210

42. Kupradze, V. D., "On approximate solution of problems in mathematical physics," Russian Math. Surveys, Vol. 22, 58-108, 1967.

43. Vekua, I. N., New Methods for Solving Elliptic Equations, North-Holland, Amsterdam, 1967.

44. Hafner, C., The Generalized Multipole Technique for Computational Electromagnetics, Artech House Books, Boston, 1990.


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